"Find the derivatives of the functions f(t)=t2−1t2+t−2" was answered by students like you

Tyra

Answered question

2021-10-20

Find the derivatives of the functions

f (t) = \frac{t^{2} - 1}{t^{2} + t - 2}

Answer & Explanation

Mitchel Aguirre

Skilled2021-10-21Added 94 answers

Step 1
Given function is:

f (t) = \frac{t^{2} - 1}{t^{2} + t - 2}

\Rightarrow f (t) = \frac{(t + 1) (t - 1)}{(t - 1) (t + 2)}

\Rightarrow f (t) = \frac{t + 1}{t + 2}

Step 2
Then the derivative of f with respect to t is derived as follows:

f^{'} (t) = \frac{d}{d t} (\frac{t + 1}{t + 2})

\Rightarrow f^{'} (t) = \frac{[\frac{d}{d t} (t + 1)] \cdot (t + 2) - (t + 1) \cdot [\frac{d}{d t} (t + 2)]}{{(t + 2)}^{2}}

\Rightarrow f^{'} (t) = \frac{1 \cdot (t + 2) - (t + 1) \cdot 1}{{(t + 2)}^{2}}

\Rightarrow f^{'} (t) = \frac{t + 2 - t - 1}{{(t + 2)}^{2}}

\Rightarrow f^{'} (t) = \frac{1}{{(t + 2)}^{2}}

Hence the answer.

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